New York mayoral candidate Bill de Blasio accepts the endorsement of the Committee of Interns and Residents, in New York City, Aug. 14, 2013. The topsy-turvy Democratic campaign for mayor took another twist on Tuesday as a new poll found that de Blasio has surged to the lead for the first time. (AP Photo/Richard Drew)

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NEW YORK—Public Advocate Bill de Blasio has opened up a significant lead in the race to become the Democratic nominee for mayor, according to a new poll.

De Blasio became the race’s surprising new front-runner earlier this month, and his surge hasn’t abated. He’s now the choice of 36 percent of likely Democratic voters, according to a Quinnipiac University poll released Wednesday.

That puts him near the 40 percent threshold that would prevent a run-off. If no candidate in the Sept. 10 primary hits that mark, the top two candidates advance to a run-off three weeks later.

The margin for second place and the other potential run-off spot is razor thin: City Council Speaker Christine Quinn is at 21 percent, while ex-comptroller Bill Thompson is at 20 percent.

De Blasio, who’s running on a more liberal platform than Quinn and Thompson, also sports big leads in hypothetical run-off matchups with his two closest rivals. He would beat Quinn, the former longtime front-runner, 59 percent to 30 percent and Thompson 52 percent to 36 percent, according to the poll.

The survey, of 602 likely Democratic primary voters, has a margin of error of 4 percentage points.

Former congressman Anthony Weiner, who briefly led the race until his support collapsed amid a new sexting scandal, has fallen to 8 percent. Comptroller John Liu is at 6.

De Blasio’s support jumped from 30 percent in a Quinnipiac poll taken Aug. 13. His momentum appears connected to an ad campaign centered on his interracial family, a widely publicized fight to keep a Brooklyn hospital open and his calls for significant reforms to the New York Police Department, which has been heavily criticized recently for its stop-and-frisk policy.

De Blasio, who’s white, leads Thompson, the race’s only black candidate, among likely black voters 34 percent to 25 percent, according to the poll. Thompson, the Democrats’ 2009 nominee, is banking on winning the majority of the black voters.

And de Blasio’s status as a Boston Red Sox fan doesn’t appear to be hurting him as only 8 percent of New Yorkers surveyed said it would make them less likely to support a candidate.

However, the race is far from over. Among those surveyed, 31 percent said there’s a “good chance” they will change their minds about a candidate in the 13 days before the primary. Also, New Yorkers traditionally settle on a candidate late and the survey included only a few days after Quinn secured the endorsement of The New York Times.

The general election, which will include the Republican nominee and independent Adolfo Carrion Jr., will be held Nov. 5.

Independent Mayor Michael Bloomberg is finishing his third term in City Hall.